An interval of a second (2nd) is the distance between 2 notes which names are in alphabetical order (A-B, B-C, C-D, D-E, E-F, F-G) and G-A, regardless of their alteration (sharp, natural or flat).
If the distance between the two notes if a step (2 half steps) then the 2nd is clasified as Major.
C-D, B-C#, Bb-C are all major 2nds.
It he distance is a half step then it’s a Minor 2nd.
B-C, C#-D, E-F are all minor 2nds.
If the distance is 1 and 1/2 step then it’s an Augmented 2nd.
Bb-C#, Gb-A, Db-E# are all augmented 2nds.
If the distance is cero step then it’s a Diminished 2nd.
B#-C, G#-Ab, D#-Eb are all diminished 2nds.
What about Gb-A#? That’s 2 steps (1/2 step bigger than an Augmented)
It is called a double-augmented 2nd.
As you can see being a 2nd does not tell us much regarding distance between notes, but just distance between names of notes.
But, why is 2+2=3?
When we stack two 2nds, one on top of each other, we get a 3rd. (C-D + D-E = C-E)
Well.. We shouldn’t be counting D twice, should we? (CDDE is actually CDE or C-E)